Respect is only part of the White Tower's problems. A lot will depend on how the last book plays out but as things stand at the moment the way the world will be looking post last battle is as follows:

The White Tower will have had a lot of new blood in the form of the novices/accepted the rebels collected. Because so many of them are older and have already established their world view they are a lot less likely to strick rididly to the old AS "That is the way things have always been done" approach and could make the White Tower more flexible.

Secondly the WT has regained a lot of lost abilities such as making ter'angreal (inperfectly) heartstone and travelling etc.

Thirdly they have established loose ties to the Wise Ones and the Windfinders and stronger ties to the Kin but neither group are firm 'allies' yet.

Against that they will have the fact that a lot of the nations will have lost their fear of the WT as the invincible machine that grinds down thrones if they get in its way. They will have seen that the WT can be hurt and people can stand up to them.

They will no longer be seen as the only way for women who want to learn the One Power to do so. I doubt if there will be a rush of people to go the Aiel or Sea Folk but the choise will be there.

The Seanchan are not going away and unless something happens in the next book they still see every Aes Sedai as someone who must be collared with an adam. They want to collar all female channelers but the Aes Sedia are their No 1 target for various historical reasons. They can now travel as well.

There is a unified male channeling orginisation that on an ordinisational level will be no friend to the Seancha but equally may not be terribly friendly to the White Tower. On an Aes Sedai Asha'man individual level there is cross bonding going on and the White Tower can probably call on male channelers to help their female Aes Sedai.

Gunpower is going to be making itself known and there may be an industrial revolution that will if not rival channeling, make it not quite as powerful as it once was for certain things.

The White Tower is going to have to engage in a very carefull balancing act to keep the nations behind them while fending off the Seanchan and trying to keep the other female channeling groups allied with them in a unified front with the Seanchan. The WT will probably also have to maintain a large standing military to off Seanchan. They don't have the resources to match teh Seanchan fully but they need to make Tar Valon enough of a fortress the Seanchan can't risk another frontal assault.

All the time this is going on they will have to keep an eye on the management of the Black Tower who might well stop any more of its members being bonded and effectivly serving the White Tower. They will also have to bear in mind that the only channeling force who have been shown to match the damane in a one power battle are the Asha'man. Even the vaulted battle ajah came off reather poorly against damane in the WT battle.

It certainly will be interesting times for Egwene and her Hall.